TransportMaps.Maps.SlicedMapBase

Module Contents

Classes

SlicedMap

Takes the map \(T({\bf x})\) and construct the map \(S_{\bf y}({\bf x}) := [T({\bf y}_{\bf i} \cup {\bf x}_{\neg{\bf i}})]_{\bf j}\), where \(S_{\bf y}:\mathbb{R}^{\sharp(\neg{\bf i})}\rightarrow\mathbb{R}^{\sharp{\bf j}}\).

class TransportMaps.Maps.SlicedMapBase.SlicedMap(**kwargs)

Bases: TransportMaps.Maps.MapBase.Map

Takes the map \(T({\bf x})\) and construct the map \(S_{\bf y}({\bf x}) := [T({\bf y}_{\bf i} \cup {\bf x}_{\neg{\bf i}})]_{\bf j}\), where \(S_{\bf y}:\mathbb{R}^{\sharp(\neg{\bf i})}\rightarrow\mathbb{R}^{\sharp{\bf j}}\).

_xin(x)

evaluate(x, **kwargs)

[Abstract] Evaluate the map \(T\) at the points \({\bf x} \in \mathbb{R}^{m \times d_x}\).

Parameters:

• x (ndarray [\(m,d_x\)]) – evaluation points

• precomp (dict) – dictionary of precomputed values

• idxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by idxs_slice must match x.shape[0].

Returns:

(ndarray [\(m,d_y\)]) – transformed points

Raises:

NotImplementedError – to be implemented in sub-classes

grad_x(x, **kwargs)

[Abstract] Evaluate the gradient \(\nabla_{\bf x}T\) at the points \({\bf x} \in \mathbb{R}^{m \times d_x}\).

Parameters:

• x (ndarray [\(m,d_x\)]) – evaluation points

• precomp (dict) – dictionary of precomputed values

• idxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by idxs_slice must match x.shape[0].

Returns:

(ndarray [\(m,d_y,d_x\)]) – transformed points

Raises:

NotImplementedError – to be implemented in sub-classes

hess_x(x, **kwargs)

[Abstract] Evaluate the Hessian \(\nabla^2_{\bf x}T\) at the points \({\bf x} \in \mathbb{R}^{m \times d_x}\).

Parameters:

• x (ndarray [\(m,d_x\)]) – evaluation points

• precomp (dict) – dictionary of precomputed values

• idxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by idxs_slice must match x.shape[0].

Returns:

(ndarray [\(m,d_y,d_x,d_x\)]) – transformed points

Raises:

NotImplementedError – to be implemented in sub-classes

action_hess_x(x, dx, **kwargs)

[Abstract] Evaluate the action of the Hessian \(\langle\nabla^2_{\bf x}T,\delta{\bf x}\rangle\) at the points \({\bf x} \in \mathbb{R}^{m \times d_x}\).

Parameters:

• x (ndarray [\(m,d_x\)]) – evaluation points

• dx (ndarray [\(m,d_x\)]) – direction on which to evaluate the Hessian

• precomp (dict) – dictionary of precomputed values

• idxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by idxs_slice must match x.shape[0].

Returns:

(ndarray [\(m,d_y,d_x\)]) – transformed points

Raises:

NotImplementedError – to be implemented in sub-classes